Global existence and blow-up solutions of the radial Schrodinger maps

This paper studies the Cauchy problem of radial inhomogeneous Schrodinger maps (ISM) which arises from the integrable model of the inhomogeneous spherically symmetric Heisenberg ferromagnetic spin system. Through a complex transformation the radial ISM is equivalent to an integro-differential Schrodinger equation. A new weighted Sobolev space ?beta 1,l(+) is introduced and the well-posedness of integro-differential Schrodinger equations, including the integral radial IMS, with small spherically symmetric initial data in one-dimensional energy space ?11,2(+) is established. Furthermore, for n <= 2, we prove the existence of blow-up solutions for the integral radial ISM.

Automated summary

This study addresses the Cauchy problem of radial inhomogeneous Schrodinger maps (ISM) through complex transformation and establishes the well-posedness of integro-differential Schrodinger equations, including the integral radial IMS, for small spherically symmetric initial data. Additionally, the existence of blow-up solutions for the integral radial ISM is proven for n <= 2.